SRC Insights: Second Quarter 2004

Management's Understanding of IRR Models

by Avi Peled, Senior Financial Specialist

Banking at its core involves understanding, pricing, and mitigating a wide variety of risks. One risk—interest rate risk—involves the estimation of the probability of adverse affects on asset or liability valuations caused by movements in interest rates. A banker must consider the affect of interest rate movements and volatility when building the bank's balance sheet by adjusting the duration and liquidity of various segments of the balance sheet. Modeling can help bank management make more informed decisions about the level of interest rate risk the institution is willing to assume.

We all use models for many purposes. In general, models allow us to view or estimate what something will look like in the future, whether an architect's model of a bank building or an econometrician's model of the economy. Bankers use models to attempt to describe in mathematical or accounting terms, often using equations (either explicitly or implicitly), a condition of their bank in the future.

Capital markets examiners examine bank models of market and trading risks. For community banks, examiners are particularly interested in the bank's ability to accurately model interest rate risks. Of perhaps equal importance is the ability of bank management, the ALCO committee, and the Board of Directors to understand the output of the model and the model's limitations. Finally, examiners are interested in seeing how bank management acts on the results of the model and how models are integrated into the strategic planning process of the institution.

Interest Rate Risk Models
In community banks, examiners generally see three types of interest rate risk models. Gap analysis, which diagrams projected cash flows into maturity/repricing buckets, gives an elementary view of interest rate risk. This can nevertheless provide useful information, especially for noncomplex institutions with limited long-term instruments and limited items with embedded options. Gap analysis usually emphasizes maturities while often failing to consider embedded options. The cash flows of assets and liabilities with options can change when interest rates change. To capture these changes, some gap reports are dynamic and reflect these cash flow changes, depending on the assumed changes in interest rates.

Earning simulations for the banking book, sometimes called Earning at Risk (EaR) models, are most often used to estimate net interest income in the one and two year time frame. EaR models are often popular with banks because they can provide an estimate of net interest income or other income measures over a one or two year horizon.

Economic Value of Equity (EVE) models (often called Market Value of Equity, MVE, or other names) are used to estimate the economic value of a banking organization.¹ Economic value is the value of the discounted cash flows of assets minus liabilities, adjusted for flows created by off balance sheet items. EaR and EVE type models can be shocked to estimate the effect of interest rate changes on the bank's future income and economic value. Usually parallel yield curve shifts are modeled in the +/- 100, 200, and 300 basis point ranges, although other magnitude movements can also be modeled. Interest rate movements can also be ramped as change occurs over time. Non-parallel yield curve changes can also be modeled to present a more realistic view of possible interest rate changes.

While interest rate risk models can be used for various purposes, including liquidity planning, budgeting, and strategic planning, examiners are mainly interested in the models as tools for market and liquidity risk assessment.

Types of Risks
There are four basic types of risk that an interest rate risk model should address—Mismatch, Yield Curve, Basis, and Options risks. Mismatch risk is the risk that assets and liabilities will reprice at different times and at different rates when interest rates change. While most banks model +/- 100, 200, and 300 basis point parallel changes in interest rates, it is highly unlikely that the yield curve will move precisely in parallel. Risk that stems from a change in the shape of the curve is referred to as yield curve risk. EaR and EVE will be affected if short-term rates move more or less than long-term rates or if the yield curve steepens or flattens, and intermediate term rates would be more or less affected when interest rates change. Factors such as these are incorporated in yield curve risk. Basis risk is the risk that rates on instruments with the same or similar maturities will not move in tandem when the general level of interest rates changes. Options risk is the risk that option holders will exercise the options implicitly or explicitly sold to them by the bank as interest rate changes make it advantageous for them to do so.

Model Construction and Inputs
A model's reflection of reality depends on how well it is constructed. Model construction involves a variety of elements, including choosing the correct variables and affirming the accuracy of the model's inputs. Management's confidence in the accuracy of the model will depend on how confident management is in its construction and the data used for inputs.

A model should be sufficiently detailed to include information on all material interest rate risks. Accounts should be combined if they will react fairly similarly to interest rate changes. However, significant accounts whose reactions to interest rate changes are not well correlated should not be aggregated but should be segregated into more specific types so that the model can capture those disparate affects.

The terms of financial instruments need to be accurately captured in a model, particularly embedded or explicit options such as calls, puts, caps, and floors. Properly reflecting the effect of embedded options for assets such as adjustable rate mortgages, which appear on many financial institutions' balance sheets, is particularly important.

Verifying model inputs is also important. Inputs should be checked to ensure that they appear reasonable and that they are entered into the model correctly. Automated data entry is preferred since it minimizes the likelihood of data input errors.

Non-maturity deposits and items with embedded options are difficult to measure. Banks have devised various methods to arrive at non-maturity deposits assumptions, ranging from estimates by line officers to sophisticated models based on data of a sampling of accounts in each deposit type spanning at least a full economic cycle.

Model Results
As noted above, the value of a model's output depends on how well the model is constructed and the accuracy of the inputs. In addition, management needs to understand how the model works and what elements go into producing its results to be able to meaningfully interpret the output.

Typical model output includes a set of numbers representing the bank's EaR or EVE under different interest rate scenarios. However, it is extremely unlikely that a specific number is 100 percent correct. Rather, if the model was properly constructed and the inputs were valid, the results should be accurate enough that management can base their IRR strategy on the results.

Bankers, especially ALCO and the Board of Directors, can take several steps to improve their understanding of the bank's model and the institution's interest rate risk.

Understand the quality of the assumptions used in the interest rate models and how the models' results could vary if assumptions were incorrect. Carefully documenting all assumptions and controlling changes to those assumptions is critical to ensure this understanding.
Understand the underlying foundation for particularly high-risk assumptions. High-risk assumptions can occur in prepayment speeds for loans and mortgage backed securities and maturity or repricing assumptions for non-maturity deposits. If private vendor estimates are used in a model, the vendor's methodology should be understood in order to evaluate its relevance for the bank and the degree of errors should be tracked.
Understand the implications of strategic planning assumptions built into the model. For EaR models, a bank may create a model based on input that reflects its strategic plan for the next year or two, rather than the current condition of the bank. These estimates should reflect reasonable assumptions concerning the economic environment and the bank's capabilities. Excessive growth rates might reflect more wishful thinking than reasonable strategic planning, particularly if forecasts of the local or national economy and the bank's past performance raise doubts that those growth rates will be met.

Improving the Quality of Model Results
Modeling assumptions can be inherently difficult to estimate. The bank's estimation methods for the assumptions may not be as advanced or as accurate as desired or some estimation techniques might require quantification and measurement skills that the bank cannot afford to acquire or obtain from private vendors. Even the most sophisticated econometric estimation models may not provide the level of accuracy required.

Estimating future behaviors can be fraught with difficulties and to some degree only limited efficiency. In essence, this is the nature of quantifying risk. However, it is important to identify those elements in the model which are least likely to be accurate and, consequently, most likely to lead to erroneous conclusions. Therefore, the first step is to identify which model assumptions are most likely to deviate in reality from the value used for model inputs.

The next step is to attempt to quantify the probability of different outcomes for the questionable assumptions. To some extent, this requires quantifying the probability of occurrence of different economic and financial conditions that could influence these outcomes. The correlation between different inputs also should be considered. For example, if loan demand fails to materialize as expected, there will probably be less need for deposit growth, so administered deposit rate changes may not be as great as originally planned.

Finally, to give ALCO and the Board of Directors an understanding of the potential effect of inaccurate assumptions on model results, the model can be run using alternate assumptions that the modeler considers less probable but still reasonable. This could mean using less favorable assumptions to develop a worst-case scenario, with the clear understanding that the assumptions are not considered the most probable but are being used to ascertain the possible range of outcomes.

One specific area where generating alternate model results could be beneficial is non-maturity deposits. Banks where non-maturity deposit valuations are substantially different from those of the federal bank regulators' benchmarks might benefit by using those benchmarks or non-maturity deposit assumptions used by similar banks in the bank's markets in place of institution-specific non-maturity deposits input estimates to develop a rough estimate of how sensitive the bank's balance sheet might be to non-maturity deposits model inputs.

Obviously, the federal bank regulators' benchmarks are only industry generalizations based upon industry observation and are not meant to replace individual bank estimates. However, when model results from using the regulators' or marketplace non-maturity deposit benchmarks vary substantially from the results when the bank's estimates are used, additional validation of the model based on institution-specific assumptions may be warranted to assure the validity of the non-maturity deposit inputs.

Using Alternate Scenarios
While bankers will use the most likely interest rate risk scenario to manage the bank's interest rate risk, they can still obtain useful information from alternate scenarios, including worst-case and best-case scenarios. The alternate outcomes can be viewed collectively to provide additional assurance of the validity of the selected scenario. For example, if the worst-case scenario and assumptions produce results not significantly different from the model with the most probable assumptions and if those results are within a bank's interest rate risk limits, then management can be fairly comfortable that even if the assumptions are off, the effect on the bank's earning potential will not be significant. If, however, results from using alternate assumptions are significantly different, prudent management may consider taking additional measures to monitor interest rate risk, develop contingency plans to manage interest rate risk if the alternate worst-case assumptions turn out to be accurate, and consider whether hedging techniques would be cost effective.

Some community bankers may question the additional time and cost needed to run models with alternate assumptions. While the actual inputs and computer runs should not take substantial additional time, identifying the important behavioral assumptions and interrelationships is probably time consuming. Hopefully, management would be considering these issues whether or not they produce alternate model runs. Even if the time and expense to produce alternate model results is prohibitive, management should at least consider the probability that their assumptions could be wrong and attempt to judge the likely deviation from the model output that they do have.

While there is no regulatory requirement for state member banks to expend the extra effort to estimate the possible range of interest rate risk caused by incorrect assumptions, this could be a useful interest rate risk management process when implemented periodically.

Additional Stress Testing
While stress testing parallel interest rate shocks up to 300 basis points may appear extreme, particularly if one is looking at instantaneous shocks, a bank could stress test its interest rate risk models periodically using ramped, non-parallel changes based on past history. For example, the fed funds rate rose by about 325 basis points between March 1988 and May 1989 and fell by about 475 basis points during 2001, while 10 year Treasuries moved relatively little over these same periods. However, from early 2001 to mid-year 2003, the 10 year Treasury rate fell over 300 basis points. Banks dependent on the current steep yield curve do not want to be surprised when the yield curve flattens. Based on the decline in interest rates over the past few years, it might be reasonable to stress test a 475 basis point or greater rise in short term interest rates ramping over a number of quarters.

One important element to consider when stress testing is whether and how traditional correlations between model components break down and what affect this has on model results. Management should not manage a bank's interest rate risk based solely on models using inputs from a stressed environment and stress scenarios; however, stress testing does provide important information for management's consideration.

Model Validation
Model validation is often a difficult exercise, although a very important one. Management often states that validating an EaR model is difficult because actual plans changed to adapt to changing circumstances over the year or two modeling period. Management also may claim that the EaR model that was validated month to month proved to be highly accurate. Considering that a bank's condition does not change that much on a monthly basis, this may not be too surprising.

Of more interest and use is an assessment of a model's accuracy over an entire year. It may be useful to compare EaR model results with actual results after one or two years, and attempt to identify the causes of any discrepancy between the modeled and actual results. The results of such an analysis might provide insight that could be used to improve the model's future performance.

EVE model results are even more difficult to validate. An institution with little change in EVE when shocked with different interest rate scenarios should demonstrate a fairly constant net interest margin (NIM). Those institutions showing significant changes in EVE and EaR when shocked under various interest rate scenarios would likewise be expected to experience variability in NIM, consistent with the model predictions.

Banks should validate the assumptions used to create the models, assessing how accurate assumptions are over time and adjusting the assumptions as needed. For example, management should be aware of any changes in its customer base or markets that would necessitate changing the way it arrives at the assumptions it uses in its models, since a change in demographics or market competition may warrant changes in model assumptions concerning non-maturity deposits.

Conclusion
Accurate interest rate risk models can provide a banking institution with a substantial advantage by providing information on the true nature of the institution's interest rate risk and allowing the institution to price and market its loans and deposits accordingly. Because of the significant percentage of model assumptions that depend on estimates of behavioral characteristics of balance sheet components, banks with significant interest rate risk or complex instruments with substantial optionality may find it useful to periodically estimate a range of results.

If you have any questions on interest rate risk modeling or interest rate risk and are supervised by the Federal Reserve Bank of Philadelphia, please contact your institution's central point of contact or assigned manager at the Reserve Bank. Questions on this article can be addressed to Avi Peled at (215) 574-6268.

¹ Bankers sometimes mistakenly believe that EVE measures liquidation value. Actually, EVE models the earnings potential of the entire balance sheet, adjusted for options and off balance sheet items.

The views expressed in this article are those of the author and are not necessarily those of this Reserve Bank or the Federal Reserve System.

SRC Insights: Second Quarter 2004

Management's Understanding of IRR Models

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